Zobrazeno 1 - 10
of 120
pro vyhledávání: '"Zhai, Zhichun"'
Partial Differential Equations (PDEs) model various physical phenomena, such as electromagnetic fields and fluid mechanics. Methods like Sparse Identification of Nonlinear Dynamics (SINDy) and PDE-Net 2.0 have been developed to identify and model PDE
Externí odkaz:
http://arxiv.org/abs/2410.18110
The primary purpose of this paper is to study the Wiener-type regularity criteria for non-linear equations driven by integro-differential operators, whose model is the fractional $p-$Laplace equation. In doing so, with the help of tools from potentia
Externí odkaz:
http://arxiv.org/abs/2309.02408
Autor:
Zhai, Zhichun
In this note, we try to understand the recent development on the Waring-Goldbach problem involving cubes of primes. Especially, we want to determine whether integers that are either primes, squares of primes, cubes of primes, or a cube of an even num
Externí odkaz:
http://arxiv.org/abs/2201.07346
Let $u(\cdot,\cdot)$ be the Caffarelli-Silvestre extension of $f.$ The first goal of this article is to establish the fractional trace type inequalities involving the Caffarelli-Silvestre extension $u(\cdot,\cdot)$ of $f.$ In doing so, firstly, we es
Externí odkaz:
http://arxiv.org/abs/2201.00765
The purpose of this article is twofold. The first is to strengthen fractional Sobolev type inequalities in Besov spaces via the classical Lorentz space. In doing so, we show that the Sobolev inequality in Besov spaces is equivalent to the fractional
Externí odkaz:
http://arxiv.org/abs/2201.00753
In this article, we investigate the robust optimal design problem for the prediction of response when the fitted regression models are only approximately specified, and observations might be missing completely at random. The intuitive idea is as foll
Externí odkaz:
http://arxiv.org/abs/2007.09317
Let $P_{\alpha} f(x,t)$ be the Caffarelli-Silvestre extension of a smooth function $f(x): \mathbb{R}^n \rightarrow \mathbb{R}^{n+1}_+:=\mathbb{R}^n\times (0,\infty).$ The purpose of this article is twofold. Firstly, we want to characterize a nonnegat
Externí odkaz:
http://arxiv.org/abs/2007.00713
Topological Data Analysis of Clostridioides difficile Infection and Fecal Microbiota Transplantation
Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a single index,
Externí odkaz:
http://arxiv.org/abs/1707.08774
Publikováno v:
Applicable Analysis; Nov2024, Vol. 103 Issue 17, p3213-3235, 23p
Autor:
Li Pengtao, Zhai Zhichun
Publikováno v:
Advances in Nonlinear Analysis, Vol 11, Iss 1, Pp 850-887 (2022)
This paper provides the Carleson characterization of the extension of fractional Sobolev spaces and Lebesgue spaces to Lq(ℝ+n+1,μ)L^q (\mathbb{R}_ + ^{n + 1} ,\mu ) via space-time fractional equations. For the extension of fractional Sobolev space
Externí odkaz:
https://doaj.org/article/65fe533da15a41a7ae576e7695b322e2